I thought the problem was more the nuclear winter that would follow nuclear war? If a volcano explosion can cause a mini-ice-age, I don't see why burning every

I thought the problem was more the nuclear winter that would follow nuclear war? If a volcano explosion can cause a mini-ice-age, I don't see why burning every major city on earth wouldn't cause enough of an ice age to cause a civilization-killing famine. Not to mention, the poisoning of substantial amounts of water, and food sources would mean that a lot of what was left over would be carcinogenic.